Limit Analysis of Notched Tension Specimens

In the authors' two theorems on limit analysis based on variational principles, the upper and the lower bounds of the safety factor are expressed in terms of functionals that can be optimized to yield the best bounds. In this paper, the proposed theorems are restated for the case of plane stress and then applied to the study of the safety factor of circular notched tension specimens. The material is assumed to be isotropic, perfectly plastic and obeys the Mises yield criterion. The study involves finding the effect of the assumed stress and velocity fields, the radius of the notch, and the height to width ratio of the specimen on both bounds. The bounds of a special case are compared to those obtained by Prager and Hodge for the same case assuming plane strain condition. Finally, the solution of the cirular notched tension specimens are modified in order to apply the results to v-notched specimens.